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In this article, we consider a discrete-time Geom/Geom/1 queue with two phase vacation policy that comprises single working vacation and multiple vacations, denoted by Geom/Geom/1/SWV+MV. For this model, we first derive the explicit expression for the stationary system size by the matrix-geometric solution method. Next, we obtain the stochastic decomposition structures of system size and the sojourn time of an arbitrary customer in steady state. Moreover, the regular busy period and busy cycle are analyzed by limiting theorem of alternative renewal process. Besides, some special cases are presented and the relationship between the Geom/Geom/1/SWV+MV queue and its continuous time counterpart is investigated. Finally, we perform several experiments to illustrate the effect of model parameters on some performance measures.
Accepté le :
DOI : 10.1051/ro/2017079
Keywords: Discrete time queue, vacation, working vacation, matrix-geometric solution, stochastic decomposition
Ye, Qingqing 1 ; Liu, Liwei 1
@article{RO_2018__52_1_95_0,
author = {Ye, Qingqing and Liu, Liwei},
title = {The analysis of discrete time {Geom/Geom/1} queue with single working vacation and multiple vacations {(Geom/Geom/1/SWV+MV)}},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {95--117},
publisher = {EDP-Sciences},
volume = {52},
number = {1},
year = {2018},
doi = {10.1051/ro/2017079},
zbl = {1393.60112},
mrnumber = {3812471},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2017079/}
}
TY - JOUR AU - Ye, Qingqing AU - Liu, Liwei TI - The analysis of discrete time Geom/Geom/1 queue with single working vacation and multiple vacations (Geom/Geom/1/SWV+MV) JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 95 EP - 117 VL - 52 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2017079/ DO - 10.1051/ro/2017079 LA - en ID - RO_2018__52_1_95_0 ER -
%0 Journal Article %A Ye, Qingqing %A Liu, Liwei %T The analysis of discrete time Geom/Geom/1 queue with single working vacation and multiple vacations (Geom/Geom/1/SWV+MV) %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 95-117 %V 52 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2017079/ %R 10.1051/ro/2017079 %G en %F RO_2018__52_1_95_0
Ye, Qingqing; Liu, Liwei. The analysis of discrete time Geom/Geom/1 queue with single working vacation and multiple vacations (Geom/Geom/1/SWV+MV). RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 95-117. doi: 10.1051/ro/2017079
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